Equal BER power control for uplink MC-CDMA with MMSE successive interference cancellation

ABSTRACT

For a given decision order, MMSE successive interference cancellation (MMSE-SIC) can simultaneously maximize SIRs of all users. To further increase its efficiency, a power control (PC) algorithm, under equal BER criterion, is disclosed for uplink MC-CDMA. In frequency-selective Rayleigh fading channels, the MMSE-SIC integrated with the equal BER PC suppresses multiple access interference (MAI) effectively, resulting in a performance very close to the single user bound (SUB).

RELATED APPLICATIONS

This application claims priority from U.S. Provisional Patentapplication Ser. No. 60/574,191, filed May 25, 2004.

GOVERNMENT LICENSE RIGHTS

The United States government may hold license and/or other rights inthis invention as a result of financial support provided by governmentalagencies in the development of aspects of the invention.

FIELD OF INVENTION

This invention relates generally to CDMA systems, and more specificallyrelates to a method for efficiently suppressing multiple accessinterferences (MAI), a major factor limiting the capacity of uplinkMC-CDMA systems.

BACKGROUND OF INVENTION

The performance of CDMA systems is limited by multiple accessinterference (MAI). Among many interference cancellation schemes,successive interference cancellation (SIC) is highly desirable, due toits low complexity, high compatibility with existing systems and easyaccommodation to strong error-correcting codes [A. J. Viterbi, “Very lowrate convolutional codes for maximum theoretical performance ofspread-spectrum multi-access channels,” IEEE J. Select Areas Commun.Vol. 8, pp. 641-649, May 1990]. However, unlike other detectiontechniques, SIC is sensitive to received power allocation. By providingchannel state information (CSI) at the receiver and reliable feedback ofpower allocation from the receiver to the transmitter, we are able tointegrate SIC with power control (PC), which can improve system capacitysignificantly.

For a system which aims to achieve comparable performance for all users,equal BER criterion is suitable for deriving the power allocation. Ashas been concluded in the literature, equal BER PC benefits SICsignificantly by increasing the reliability of earlier detected users.Nevertheless, most of the work focused on (match filter) SIC (MF-SIC)[Viterbi op. cit.; G. Mazzini “Equal BER with successive interferencecancellation DS-CDMA systems on AWGN and Ricean channels,” in Proc. ICCCPIMRC, July 1995, pp. 727-731; R. M. Buehrer, “Equal BER performance inlinear successive interference cancellation for CDMA systems,” IEEETrans. Commun., vol. 49, no. 7, pp 1250-1258, Jul. 2001]. With theincrease of system load, in CDMA systems, the performance of MF degradesquickly, limiting the effectiveness of SIC. Therefore, it is meaningfulto integrate PC with SIC for more powerful detection techniques, such asdecorrelating and MMSE. For a given decision order, MMSE SIC (MMSE-SIC)maximizes all users' SIRs simultaneously [T. Guess, “Optimal sequencesfor CDMA with decision-feedback receivers,” IEEE Trans. Commun., vol.,49, pp. 886-900, Apr. 2003]. Therefore, in this invention we considerthe equal BER PC algorithm for this optimal SIC receiver inquasi-synchronous uplink MC-CDMA.

SUMMARY OF INVENTION

For a given decision order, MMSE successive interference cancellation(MMSE-SIC) can simultaneously maximize SIRs of all users [T. Guess Op.cit.]. To further increase its efficiency, a power control (PC)algorithm, under equal BER criterion, is used in this invention foruplink MC-CDMA. In frequency-selective Rayleigh fading channels, theMMSE-SIC integrated with the equal BER PC suppresses multiple accessinterference (MAI) effectively, resulting in a performance very close tothe single user bound (SUB). In the present invention a method is thusdisclosed for efficiently suppressing multiple access interference(MAI), a major factor limiting the capacity of uplink MC-CDMA systems. Anovel power control algorithm is used under equal BER criterion for anonlinear MMSE-SIC receiver.

BRIEF DESCRIPTION OF DRAWINGS

The invention is illustrated by way of example in the drawings appendedhereto in which:

FIG. 1 is a schematic block diagram of an MC-CDMA system in accordancewith the invention, with MMSE receiver integrated with the equal BER PC;

FIG. 2 is a graph of BER performance, with different receiverstructures, with and without PC, over 16 users versus the averageE_(b)/N₀ per user; and

FIG. 3 is a graph of BER performance, with different receiverstructures, with and without PC, over 16 users versus the averageE_(b)/N₀ per user.

DESCRIPTION OF PREFERRED EMBODIMENT

In FIG. 1 a block diagram of the MC-CDMA system with MMSE-SIC receiverintegrated with the equal BER PC is schematically depicted. Referring tothe Figure, the method comprises the following steps:

-   (a) Based on the channel state information (CSI) obtained at the    receiver, the “Equal BER Power Control” block is employed to    calculate the transmit power allocation of different users. A    successive algorithm is used, which searches the transmit power of    different users under Equal BER criterion with a total transmit    power constraint (the “Multi-carrier Channel Model” represents a    concatenation of IDFT, wireless fading channel and DFT).-   (b) With the assumption of slow fading channel, the calculated power    allocation is fed back to the transmitter so that each user will    transmit with the assigned power. (b denotes a vector including    transmit symbols of all users.)-   (c) At the receiver, the non-linear MMSE-SIC receiver is employed.    (The block diagram of FIG. 1 shows a standard operation of the    non-linear MMSE-SIC receiver. The output of DFT x is first processed    with a Matched-Filter Bank. Then, the output y is processed by a    feedforward matrix F. After that, based on a certain decision order    and output z, a “Hard Decision Device” is used to make decisions on    certain transmit symbols with MMSE criterion and the earlier    detected symbols {circumflex over (b)} are fed back through a    feedback matrix B to assist in detecting other symbols.) The equal    BER power control ensures that different users achieve the same    signal-to-interference (SIR) ratio after SIC, hence, significantly    improving the performance of SIC and effectively suppressing MAI.

By properly defining the search district and with some well-known searchalgorithms, only a small number of searches are required for eachchannel realization. Therefore, this power control algorithm has a lowcomplexity, particularly under a slow fading channel.

Simulation results show that the MAI can be suppressed effectively,resulting in a performance very close to the theoretical limit MMSE-SICReceiver for MC-CDMA.

In quasi-synchronous uplink MC-CDMA, with total N sub-carriers and Kactive users, for the k^(th) user, each transmit symbol is replicatedinto N copies and each copy is multiplied by a chip of a preassignedspreading code c_(k) of length N (frequency domain spreading). Aftertransforming by an N-point IDFT and parallel-to-serial (P/S) conversion,a cyclic prefix (CP) is inserted between successive OFDM symbols toavoid inter-symbol interference (ISI). Finally, after RF upconversion,the signal is transmitted through the channel [S. Hara and R. Prasad,“Overview of multicarrier CDMA,” IEEE Commun. Mag., Vol. 35, no. 12, pp.126-133, December 1997].

A frequency-selective Rayleigh fading channel is considered. However,with the use of CP, the channel can be considered frequency-nonselectiveover each sub-carrier [Z. Wang and G. B. Giannakis, “Wirelessmulticarrier communications where Fourier meets Shannon,” IEEE SignalProcessing Mag., pp. 29-48, May 2000]. We assume time-invariant duringeach OFDM symbol, hence, the channel for the k^(th) user can berepresented by an (N×1) vector, h_(k)=[h_(k,1),h_(k,2), . . .,h_(k,N)]^(T), where each element is a complex Gaussian random variablewith unit variance. Furthermore, due to the proximity and partialoverlap of signal spectra, correlated fading on different sub-carriersis considered. The correlation between two sub-carriers depends on theirfrequency spacing and the RMS channel delay spread τ_(d) [W. C. Jackes,Microwave Mobile Communications. New York: Wiley, 1974].

After discarding the CP, the received signal is demodulated by anN-point DFT, and the output during the i^(th) OFDM symbol interval canbe expressed in a compact matrix form asx(i)={tilde over (C)}Ab(i)+η(i),where {tilde over (C)}=[h₁·c₁, h₂·c₂, . . . , h_(K)·c_(K)] denotes thechannel-modified spreading code matrix, with · representing element-wisemultiplication; A=diag(a₁,a₂, . . . ,a_(K)) is a diagonal matrixcontaining the received amplitudes of all users and b(i)=[b₁(i), b₂(i),. . . , b_(K)(i)]^(T) containing all parallel transmitted symbols, whichare assumed BPSK modulated with normalized power; The (N×1) whiteGaussian noise vector η(i) has zero mean and covariance matrix σ²I,where I is an (N×N) identity matrix.After match filtering, we havey(i)={tilde over (C)} ^(H) ·x(i)=RAb(i)+{tilde over (η)}(i),where R={tilde over (C)}^(H){tilde over (C)} is the channel-modifiedcross correlation matrix. The MMSE-SIC receiver is implemented using theCholesky factorization (CF) of the positive definite matrixR_(m)=R+σ²A⁻², which can be uniquely decomposed as R_(m)=Γ^(H)D²Γ, withΓ upper triangular and monic (having all ones along the diagonal) andD²=diag([d₁ ², d₂ ², . . . , d_(K) ²]^(T)) having positive elements onits diagonal. Multiplying on both sides of equation (yy) by D⁻²Γ^(−H),we obtainz(i)=D ⁻²Γ^(−H) ·y(i)=ΓAb(i)+{circumflex over (η)}(i),where {circumflex over (η)}(i) is a (K×1) vector with uncorrelatedcomponents, (Note that the extra term −D⁻²Γ^(−H)σ²A⁻¹b(i) was includedinto {circumflex over (η)}(i).) whose covariance matrixR_({circumflex over (η)}(i))=σ²D⁻² [G. Ginis and J. Cioffi, “On therelationship between V-BLAST and the GDFE,” IEEE Commun. Lett., vol. 5,pp. 364-366, September 2001]. Since Γ is upper triangular and{circumflex over (η)}(i) has uncorrelated components, b(i) can berecovered by back-substitution combined with symbol-by-symbol detection.The detection algorithm is as follows,

for  k = 0  to  K − 1${{\hat{b}}_{K - k}(i)} = {{hard}\mspace{14mu}{{decision}\left( {\left( {z_{K - k}(i)} \right) - {\sum\limits_{m = 1}^{k}{{a_{K - {k_{+}m}} \cdot \Gamma_{{K - k},{K - {k_{+}m}}}}{{\hat{b}}_{K - {k_{+}m}}(i)}}}} \right)}}$By ignoring decision errors (It is pointed out in [Guess op. cit.] thatin uncoded systems, the effects of error propagation can for the mostpart be mitigated, when the users are detected in decreasing order ofSIR) the SIR of the (k+1)^(th) detected symbol {circumflex over(b)}_(K-k)(i) can be expressed as [G. K. Kaleh, “Channel equalizationfor block transmission systems,” IEEE J. Select Areas Commun., vol. 13,pp. 110-121, January 1995]:

${SIR}_{K - k} = {{\frac{E\left\lbrack {{a_{K - k}{b_{K - k}(i)}}}^{2} \right\rbrack}{mmse} - 1} = {\frac{a_{K - k}^{2}}{\sigma^{2}d_{K - k}^{- 2}} - 1.}}$Moreover, when all interferences are cancelled, the last detected symbol{circumflex over (b)}₁(i) achieves the single user bound (SUB), given by

${{BER}_{SUB} = {E_{H}\left\lbrack {Q\left( \sqrt{\frac{a_{1}^{2} \cdot \left( {\frac{1}{N}{\sum\limits_{n = 1}^{N}{h}_{1,n}^{2}}} \right)}{\sigma^{2}}} \right)} \right\rbrack}},$where E_(H)[·] denotes the expectation over all channel realizations andQ(·) represents the tail of the error function.

Equal BER PC Algorithm

From (snr), to achieve the same BER, for all users, we needa _(K) ² d _(K) ² =a _(K-1) ² d _(K-1) ² = . . . =a ₁ ² d ₁ ².Expressing R_(m)=R+σ²A⁻² and its CF, R_(m)=Γ^(H)D²Γ in details, we getthe following two equal matrices,

${\begin{bmatrix}{r_{1,1} + {\sigma^{2}a_{1}^{- 2}}} & r_{1,2} & \ldots & r_{1,K} \\r_{2,1} & {r_{2,2} + {\sigma^{2}a_{2}^{- 2}}} & \ldots & r_{2,k} \\\vdots & \vdots & ⋰ & \vdots \\r_{K,1} & r_{K,2} & \ldots & {r_{K,K} + {\sigma^{2}a_{K}^{- 2}}}\end{bmatrix}\mspace{14mu}{{and}\begin{bmatrix}d_{1}^{2} & {d_{1}^{2}\gamma_{1,2}} & \ldots & {d_{1}^{2}\gamma_{1,K}} \\{d_{1}^{2}\gamma_{1,2}^{*}} & {\sum\limits_{k = 1}^{2}{d_{k}^{2}{\gamma_{k,2}}^{2}}} & \ldots & {\sum\limits_{k = 1}^{2}{d_{k}^{2}\gamma_{k,K}\gamma_{k,2}}} \\\vdots & \vdots & ⋰ & \vdots \\{d_{1}^{2}\gamma_{1,K}^{*}} & {\sum\limits_{k = 1}^{2}{d_{k}^{2}\gamma_{k,K}^{*}\gamma_{k,2}}} & \ldots & {\sum\limits_{k = 1}^{K}{d_{k}^{2}{\gamma_{k,K}}^{2}}}\end{bmatrix}}},$where * denotes complex conjugate, r_(ij) and γ_(ij) denote the(i,j)^(th) element of R and Γ, respectively. Notice γ_(ij)=1 when i=j.Since R_(m) is Hermitian symmetric, we only consider the lower triangle.Defining a_(k) ²d_(k) ²

λ, then (snr) becomes

${SIR}_{k} = {\frac{\lambda}{\sigma^{2}} - 1}$(k=1, 2, . . . , K), which greater than zero for λ>σ². By equating thefirst column of (m1) and (m2), we obtain the following K equations

$\left\{ {\begin{matrix}{{r_{1,1} + {\sigma^{2}a_{1}^{- 2}}} = d_{1}^{2}} \\{r_{2,1} = {d_{1}^{2}\gamma_{1,2}^{*}}} \\\vdots \\{r_{K,1} = {d_{1}^{2}\gamma_{1,K}^{*}}}\end{matrix}.} \right.$Substituting

$d_{1}^{2} = \frac{\lambda}{a_{1}^{2}}$into the first equation of (e1), we get

$a_{1}^{2} = {{\frac{\lambda - \sigma^{2}}{r_{1,1}}\mspace{14mu}{and}\mspace{14mu} d_{1}^{2}} = {\frac{\lambda\; r_{1,1}}{\lambda - \sigma^{2}}.}}$Applying d₁ ² in the rest equations, we obtain

$\gamma_{1,k} = \frac{r_{k,1}^{*}}{d_{1}^{2}}$(k=2, 3, . . . , K). Similarly, from the K−1 equations of the secondcolumn, we get

$a_{2}^{2} = {\frac{\lambda - \sigma^{2}}{r_{2,2} - {{\gamma_{1,2}}^{2}d_{1}^{2}}}.}$With

$d_{2}^{2} = \frac{\lambda}{a_{2}^{2}}$and the results obtained from the first column, γ_(2,k) (k=3, 4, . . . ,K) can be solved. Applying the same method successively for the restcolumns, finally, we obtain the power allocation a_(k) ², which can beexpressed in the general successive form as

$\left\{ \begin{matrix}{a_{1}^{2} = \frac{\lambda - \sigma^{2}}{r_{1,1}}} \\{a_{k}^{2} = {\frac{\lambda - \sigma^{2}}{r_{k,k} - {\sum\limits_{j = 1}^{k - 1}{{\gamma_{j,k}}^{2}a_{j}^{- 2}\lambda}}}{\left( {{k = 2},\ldots\mspace{11mu},K} \right).}}}\end{matrix}\quad \right.$From (result), a_(k) ² (k=1, 2, . . . , K) is a function of λ, is whichwas proven in Appendix A to satisfy the following property: a_(k)²ε[0,+∞) (k=1, 2, . . . , K) are monotonically increasing withλε[σ²,+∞). With the above conclusion, under a power constraint ρε[0,+∞), there uniquely exists a (λ)^(†), and with (result), a unique powerdistribution (a_(k) ²)^(†), which satisfies

$\mathcal{P} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}{\left( a_{k}^{2} \right)^{\dagger}.}}}$In conclusion, the algorithm can be described as follows: 1) let λ=σ² 2)applying (result), calculate

$\frac{1}{K}{\sum\limits_{k = 1}^{K}{a_{k}^{2}.}}$3) compare the result with ρ, if smaller, increase λ and go back to step2) until finally

$\mathcal{P} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}a_{k}^{2}}}$with predefined accuracy By properly defining the range of λ and withsome well-known search algorithms, the number of searches can be reducedsignificantly. A modified CF algorithm might possibly be needed if thechannel changes very fast. Since decision errors were ignored, theactually achieved SIR will be lower than the expected, which equals

$\frac{(\lambda)^{\prime}}{\sigma^{2}} - 1.$Therefore, the following expression is a BER lower bound (LB) forMMSE-SIC receiver with the equal BER PC

${BER}_{LB} = {{E_{H}\left\lbrack {Q\left( \sqrt{\frac{(\lambda)^{\dagger}}{2} - 1} \right)} \right\rbrack}.}$

Simulation Results and Discussions

An indoor Rayleigh fading channel model is employed for simulations,with 100 MHz total bandwidth and τ_(d)=25 ns. The sub-carrier number Nis chosen to be 16. Orthogonal Walsh Hadamard codes are employed forspreading. For each user, the instantaneous channel is randomly chosenfrom an ensemble consisted of 1000 i.i.d. Rayleigh fading channels(assumed unchanged for 100 symbols).

To emphasize the performance improvement with the proposed scheme, wecompare in FIG. 2 the average BER performance, with different receiverstructures, with and without PC, over 16 users versus the averageE_(b)/N₀ per user. From this figure, we can see that the performance ofMF (no SIC) ((a)) and MF-SIC with equal received power ((b)) are heavilylimited by MAI, while MMSE (no SIC) ((d)) handles MAI much better thanMF ((a) or (b)). Even with equal received power, employing SIC to MMSE((e)) results in a significant performance improvement. Nevertheless, ata BER of 10⁻⁴, it is about 10 dB worse than the SUB ((h), equation (6)).Integrating MMSE-SIC with the proposed equal BER PC ((f)), additional 8dB improvement can be obtained at a BER of 10⁻⁴, which is only less than2 dB worse than the SUB, and it significantly outperforms MF-SIC withthe equal BER PC ((c)). Moreover, it is interesting to note that theperformance difference between the simulation result with MMSE-SIC withthe equal BER PC ((f)) and the LB ((g), equation (13)) is very small,especially at high E_(b)/N₀, which justifies the assumption of ignoringdecision errors.

FIG. 3 shows the received power allocation (averaged over 1000 channels,σ²=1) on 16 successive detected users. Not surprisingly, under differentE_(b)/N₀, earlier detected users (larger index) are always allocatedmore power than the later detected ones (smaller index).

Under equal BER criterion, the PC algorithm disclosed for the MMSE-SICreceiver and its performance is thus analyzed and compared with otherreceiver strategies with and without PC in frequency-selective Rayleighfading channels. From the results, we conclude that MMSE-SIC integratedwith the equal BER PC is a powerful solution for suppressing MAI inuplink MC-CDMA systems.

Appendix A

Proof of Property that: a_(k) ²ε[0, +∞) (k=1, 2, . . . , K) aremonotonically increasing

with λε[σ²,+∞)

Proof: Clearly, when λ=σ², a_(k) ²=0 (k=1, 2, . . . , K). When ignoringdecision errors, the k^(th) detected symbol is only interfered by thosehaven't been detected ((k+1)^(th), (k+2)^(th), . . . , K^(th)) and itsSIR can be expressed alternatively as SIR_(K-k+1)=a_(K-k+)1²{tilde over(C)}_(K-k+)1^(H)S_(K-k+)1⁻¹{tilde over (C)}_(K-k+)1, where

$S_{K - k + 1} = {{\sum\limits_{j < k}{{\overset{\sim}{C}}_{K - j + 1}a_{K - j + 1}^{2}{\overset{\sim}{C}}_{K - j + 1}^{H}}} + {\sigma_{n}^{2}I}}$and X_(k) denotes the k^(th) column of matrix X. For the last (K^(th))detected symbol, since all interference has been perfectly cancelled,

${SIR}_{1} = {{\frac{\lambda}{\sigma^{2}} - 1} = {\frac{a_{1}^{2}{\overset{\sim}{C}}_{1}^{H}{\overset{\sim}{C}}_{1}}{\sigma^{2}}.}}$Clearly, a₁ ² is monotonically increasing with λ. In another word, withλ₁>λ₂, a_(1|λ) ₁ ²>a_(1|λ) ₂ ². For the second last ((K−1)^(th))detected symbol,

${{SIR}_{2} = {{\frac{\lambda}{\sigma^{2}} - 1} = {a_{2}^{2}{\overset{\sim}{C}}_{2}^{H}S_{2}^{- 1}{\overset{\sim}{C}}_{2}}}},$where S₂={tilde over (C)}₁a₁ ²{tilde over (C)}₁ ^(H)+σ²I. When λ₁>λ₂,a_(1|λ) ₁ ²>a_(1|λ) ₂ ², hence, S_(2|λ) ₁ −S_(2|λ) ₂ is positivedefinite, which means S_(2|λ) ₁

S_(2|λ) ₂ . Obviously, (S_(2|λ) ₁ )⁻¹

(S_(2|λ) ₂ )⁻¹, thus, {tilde over (C)}₂ ^(H)((S_(2|λ) ₁ )⁻¹−(S_(2|λ) ₂)⁻¹){tilde over (C)}₂<0. If

${a_{2|\lambda_{1}}^{2} \leq a_{2|\lambda_{2}}^{2}},{{\frac{\lambda_{1}}{\sigma^{2}} - 1} \leq {\frac{\lambda_{2}}{\sigma^{2}} - 1}},$which conflicts with λ₁>λ₂. Therefore, to achieve a higher SIR (largerλ), a₂ ² must be increased to compensate for higher interference, whichmeans, a₂ ² is also monotonically increasing with λ. Similar analysiscan be made successively for the other symbols.

While the present invention has been described in terms of specificembodiments thereof, it will be understood in view of the presentdisclosure, that numerous variations upon the invention are now enabledto those skilled in the art, which variations yet reside within thescope of the present teaching. Accordingly, the invention is to bebroadly construed, and limited only by the scope and spirit of theclaims now appended hereto.

1. A method for efficiently suppressing multiple access interference(MAI) in an uplink multi-carrier code-division multiple-access (MC-CDMA)system, comprising: integrating a nonlinear minimum mean-squareerror-successive interference cancellation (MMSE-SIC) receiver in saidsystem with an equal bit-error rate (BER) power control (BER PC) tocontrol transmit power of multiple users on the uplink, wherein, basedon channel state information (CSI) obtained at the receiver, transmitpower allocations of said multiple users are calculated by use of asuccessive algorithm that searches the transmit power of said multipleusers under an equal BER criterion with a total transmit powerconstraint.
 2. A method in accordance with claim 1, wherein said systemconsiders slow fading channels and a given decision order, for which thenonlinear MMSE-SIC receiver maximizes said multiple users'signal-to-interference ratios (SIRs) simultaneously.
 3. A method inaccordance with claim 1, wherein at least one calculated powerallocation is fed back to a transmitter so that a user of saidtransmitter will transmit with an assigned power.
 4. A method inaccordance with claim 1, wherein the power allocation of a k^(th) user,a_(k) ², is expressed in general successive form as $\begin{matrix}\left\{ {\begin{matrix}{a_{1}^{2} = \frac{\lambda - \sigma^{2}}{r_{1,1}}} \\{a_{k}^{2} = {\frac{\lambda - \sigma^{2}}{r_{k,k} - {\sum\limits_{j = 1}^{k - 1}{{\gamma_{j,k}}^{2}{a\;}_{j}^{- 2}\lambda}}}\left( {{k = 2},\ldots\;,K} \right)}}\end{matrix},} \right. & {{Equation}\mspace{14mu}(A)}\end{matrix}$ where K is the number of active users; where σ² denotesthe noise variance; r_(i,j) denotes the (i,j)^(th) element of R, where Ris the channel-modified cross correlation matrix; Υ_(ij) denotes the(ij)^(th) element of r, which is obtained from the Choleskyfactorization (CF) of the positive definite matrix R_(m)=R+σ²A⁻² , whereA =diag (a₁, a₂, . . . , a _(k)) is a diagonal matrix containing thereceived amplitudes of all users; the said CF enabling R_(m) to beuniquely decomposed to be R_(m)=Γ^(H) D²Γ, where Γ is upper triangularand monic and D²is diagonal with all positive elements, D²=diag([d₁ ²,d₂², . . . ,d_(<) ²]^(T)); and wherein the algorithm is implemented by thesteps of 1) letting λ=σ²; 2) applying Equation (A) to calculate1/KΣ_(k=1) ^(K) a_(k) ².; 3) comparing the result with the powerconstraint P, and if smaller, increasing λ and going back to step 2)until finally P=1/KΣ_(k=1) ^(K) a_(k) ² with predetermined accuracy. 5.A method of suppressing multiple access interference (MAI) in an uplinkmulti-carrier code-division multiple-access (MC-CDMA) communicationsystem, the method comprising: demodulating a received MC-CDMA signalusing non-linear minimum mean-square error/successive interferencecancellation reception (MMSE-SIC); and determining transmit powerallocations for multiple uplink transmitters based on an equal bit-errorrate (BER) power control scheme, wherein said equal BER power controlscheme utilizes channel state information obtained from the receivedMC-CDMA signal, and wherein said determining comprises: using aniterative algorithm to search transmit powers of the multiple uplinktransmitters according to an equal BER criterion with a total transmitpower constraint.
 6. The method according to claim 5, wherein saiddemodulating comprises: simultaneously maximizing signal-to-interferenceratios corresponding to signals received from the multiple uplinktransmitters.
 7. The method according to claim 5, wherein said iterativealgorithm comprises: (a) letting λ=σ²; (b) applying Equation (A) tocalculate ${\frac{1}{K}{\sum\limits_{k = 1}^{K}{a_{k}^{2}.}}};$ (c)comparing the result obtained in (b) with the power constraint P, and ifsmaller, increasing λ and going back to step (b) until finally$\overset{\_}{P} = {\frac{1}{K}{\sum\limits_{k = 1}^{K}\; a_{k}^{2}}}$ with predetermined accuracy, wherein a_(k) ² represents the transmitpower allocation of the k^(th) uplink transmitter and Equation (A) isdefined as follows: $\begin{matrix}\left\{ {\begin{matrix}{a_{1}^{2} = \frac{\lambda - \sigma^{2}}{r_{1,1}}} \\{a_{k}^{2} = {\frac{\lambda - \sigma^{2}}{r_{k,k} - {\sum\limits_{j = 1}^{k - 1}{{{{\gamma\; j},k}}^{2}a_{j}^{- 2}\lambda}}}\left( {{k = 2},\ldots\mspace{11mu},K} \right)}}\end{matrix},} \right. & {{Equation}\mspace{14mu}(A)}\end{matrix}$ where K is the number of active uplink transmitters; σ²denotes noise variance; r_(i,j) denotes the (i,j)^(th) element of R,where R is the channel-modified cross-correlation matrix; γij denotesthe (i,j)^(th) element of r, which is obtained from the Choleskyfactorization (CF) of the positive definite matrix R_(m)=R+σ²A⁻², whereA =diag (a₁,a₂, . . . a_(K))is a diagonal matrix containing the receivedamplitudes of the signals corresponding to the K active transmitters;the CF enabling R_(m) to be uniquely decomposed to be R_(m)=Γ^(H)D²Γ,where Γ is upper triangular and monic and D² is diagonal with allpositive elements, D²=diag([d₁ ²,d₂ ², . . . ,d_(<) ²]^(T)).
 8. Themethod according to claim 5, further comprising: feeding back thetransmit power allocations to the multiple uplink transmitters.
 9. Areceiver for a multi-carrier code-division multiple-access (MC-CDMA)signal, the receiver comprising: a non-linear minimum mean-squareerror/successive interference cancellation (MMSE-SIC) module to extractdata from a received MC-CDMA signal; and an equal bit-error rate (BER)power control calculator to calculate transmit power allocations formultiple transmitters transmitting component signals of the receivedMC-CDMA signal, wherein the equal BER power control calculator isfurther to utilize channel state information obtained based on thereceived MC-CDMA signal, and wherein said equal BER power controlcalculator is to use an iterative algorithm to search transmit powers ofthe multiple transmitters according to an equal BER criterion with atotal transmit power constraint.
 10. The receiver according to claim 9,wherein said iterative algorithm comprises: (a) letting λ=σ²; (b)applying Equation (A) to calculate 1/K Σ_(k=1) ^(K)a_(k) ².; (c)comparing the result obtained in (b) with the power constraint P, and ifsmaller, increasing λ and going back to step (b) until finally P =1/KΣ_(k=1) ^(K)a_(k) ² with predetermined accuracy, wherein a_(k) ²represents the transmit power allocation of the k^(th) transmitter andEquation (A) is defined as follows: $\begin{matrix}\left\{ {\begin{matrix}{a_{1}^{2} = \frac{\lambda - \sigma^{2}}{r_{1,1}}} \\{a_{k}^{2} = {\frac{\lambda - \sigma^{2}}{r_{k,k} - {\sum\limits_{j = 1}^{k - 1}{{{{\gamma\; j},k}}^{2}a_{j}^{- 2}\lambda}}}\left( {{k = 2},\ldots\mspace{14mu},K} \right)}}\end{matrix},} \right. & {{Equation}\mspace{14mu}(A)}\end{matrix}$  where K is the number of active transmitters; σ² denotesnoise variance; r_(i,j) denotes the (i,j)^(th) element of R, where R isthe channel-modified cross-correlation matrix; γij denotes the(i,j)^(th) element of r, which is obtained from the Choleskyfactorization (CF) of the positive definite matrix R_(m)=R+σ²A⁻², whereA =diag(a₁,a₂, . . . , a_(K)) is a diagonal matrix containing thereceived amplitudes of the signals corresponding to the K activetransmitters; the CF enabling R_(m) to be uniquely decomposed to beR_(m)=Γ^(H)D²Γ, where Γ is upper triangular and monic D² is diagonalwith all positive elements, D²=diag([d₁ ²,d₂ ², . . . , d_(<) ²]^(T)).11. The receiver according to claim 9, further comprising: a feedbackchannel to provide the transmit power allocations to the transmitters.12. The receiver according to claim 9, wherein said MMSE-SIC modulecomprises: a matched filter bank to process the received MC-CDMA signalto obtain a processed received signal vector; a feed-forward matrixmultiplier to multiply the processed received signal vector by afeed-forward matrix to obtain a further signal vector; and a decisionblock to process the further signal vector to obtain an output datavector.
 13. The receiver according to claim 12, wherein the decisionblock comprises: a summation device to receive the further signalvector; an MMSE decision device to provide said output data vector; anda feedback path to multiply the output data vector by a feedback matrixand to provide the result to said summation device.